First, check you menu settings for (High Definition Media Interface) HDMI on your TV and on your home theater system, if they are correct then, I have bad news the HDMI port on your TV or on your home theater system has been blown. This is a common and on-going problem with HDMI. The control circuitry is suceptable to stray voltages, which cause the HDMI IC and circuit to malfunction.
I would suggest if it is the HDMI port, having a qualified TV technician troubleshoot the problem and give you an estimate on the cost of repair.
However if you want to try to do this yourself, here is what you will need:
1) schematic of the TV
3) Oscilloscope (optional)
4) HDMI signal generator (This can be improvised if you have a background in electroniocs)
First unplug the TV and remove the back cover. Then using the schematic find the voltage rail that suppllies voltage to the HDMI port. Plug the tv back in and turn it on. Using the multimeter set to DC volts measure the voltage on the HDMI port control IC and compare it to the schematic values, if they are different within 10% then you have a problem with the IC and it needs to be changed out. If there is no DC voltage difference the look deeper into the circuitry, and follow the path to the main processor, checking the voltages and comparing them to the schematic values. If this proves to be unsuccessful, use the oscilloscope to look at the wave forms (These will be digital pulses) and compare them to the schematic values (they should be as close as possible to the schematic values).
Once you determine that the problem is in the HDMI IC you will need to remove the IC by desoldering it. After the IC is removed clean the area and then replace it with a new HDMI IC.
If you need asistance with the process let me know and I'll try to walk you through it. The best bet however is to call a TV technician.
I hope this helps,